The suggestion that breastfeeding may keep babies' blood pressure down - for life - may have been premature.
There are undisputed benefits to breastfeeding
Researchers from St George's Hospital in south London looked at a number of studies which made the claim.
Writing in the British Medical Journal, they say that the findings of some of them might be unreliable, exaggerating the potential benefits.
However, experts say there remain plenty of other health reasons to breastfeed a baby where possible.
The researchers pooled the results of 29 research papers which looked at links between adult blood pressure and whether the patient had been breastfed as a baby.
Smaller studies suggested quite a strong link between lower blood pressure in adulthood and breastfeeding.
High blood pressure has been linked to the development of heart disease.
However, the larger the study, the less likely it was to show a marked effect.
The St George's team suggest that smaller studies that failed to show a result in favour of breastfeeding would probably have been harder to get published in research journals - leading to bias in favour of those which did show an effect.
They wrote: "Our analysis suggests that any effect of breastfeeding on blood pressure is modest and of limited clinical or public health importance.
"However, blood pressure is not the only relevant outcome - the case for breastfeeding rests on a combination of long and short term benefits."
Other evidence has suggested that breastfed babies are less likely to become obese in later life - although the precise reason still eludes researchers. They are also less likely to have raised cholesterol levels.
The potential anti-obesity effect has recently been challenged by two studies - also in the British Medical Journal - which suggested that no link exists.
There is also evidence that breastfed babies may enjoy some measure of protection against allergic diseases such as eczema and asthma.
These babies are also less likely to suffer certain infections or be hospitalised with diarrhoeal illnesses.
In the short term, breastfeeding is said to help establish the mother-child bond.
Benefits for breastfeeding mothers include a reduced risk of certain types of cancer.
A spokesman for the National Childbirth Trust said that there were clear benefits to breastfeeding.
She said: "It's not a case of trying to justify breastfeeding by talking about these long and short-term benefits.
"Breastfeeding is justified because it is the natural way of feeding a baby."